To determine which ordered pairs represent points on the line described by the equation \( y = \frac{1}{4}x + \frac{1}{2} \), we'll substitute each x-value in the ordered pairs and see if the resulting y-value matches the y-value in the pair.
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For \( (3, 1) \): \[ y = \frac{1}{4}(3) + \frac{1}{2} = \frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \quad \text{(not equal to 1)} \] Result: Not on the line
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For \( (0, 0.5) \): \[ y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = \frac{1}{2} \quad \text{(equal to 0.5)} \] Result: On the line
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For \( (0, -2) \): \[ y = \frac{1}{4}(0) + \frac{1}{2} = 0 + \frac{1}{2} = \frac{1}{2} \quad \text{(not equal to -2)} \] Result: Not on the line
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For \( (-2, 0) \): \[ y = \frac{1}{4}(-2) + \frac{1}{2} = -\frac{1}{2} + \frac{1}{2} = 0 \quad \text{(equal to 0)} \] Result: On the line
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For \( (2, 1) \): \[ y = \frac{1}{4}(2) + \frac{1}{2} = \frac{1}{2} + \frac{1}{2} = 1 \quad \text{(equal to 1)} \] Result: On the line
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For \( (6, 2) \): \[ y = \frac{1}{4}(6) + \frac{1}{2} = \frac{3}{2} + \frac{1}{2} = \frac{4}{2} = 2 \quad \text{(equal to 2)} \] Result: On the line
Based on the calculations, the ordered pairs that are on the line \( y = \frac{1}{4}x + \frac{1}{2} \) are:
- \( (0, 0.5) \)
- \( (-2, 0) \)
- \( (2, 1) \)
- \( (6, 2) \)
Final Selected Ordered Pairs:
- \( (0, 0.5) \)
- \( (-2, 0) \)
- \( (2, 1) \)
- \( (6, 2) \)